What is an axiom?

1. In De Corpore, Hobbes writes: ‘A primary proposition is one in which the predicate is a name which explains the subject by means of a number of names.’ The example immediately given is the primary proposition: ‘A human is a rational, animated body’, which progressively reveals multiple determinations or aspects of the single given subject, in this case a human. This, Hobbes tells us, is what it is to be a definition, and the sense of such claims constitute truths that are indemonstrable in principle. He goes on: ‘There are some who add certain other propositions, which they call “primary” or “principles”, namely axioms or common notions. However, they are not really principles, because they can be proved (even if their self-evidence means that they do not need to be proved).’ (Hobbes, De Corpore, §3.9) And yet it is not clear how an axiom or common notion would be proven, since they are neither propositions nor definitions. Continue reading “What is an axiom?”